Modeling eyes for a manifold and continuous game asset?
It won't be non-manifold ; a manifold mesh can have holes.

It will intersect, unless you make sure the socket contour is perfectly adjusted to the eyeball (you can use surface snap, or maybe a shrinkwrap modifier). Intersect isn't really an issue in the vast majority of real time engine ; in fact, it's often used to save up polys.

An other technique is to model only the visible part of the eye (make the eye a bump in the face, like a statue or a sculpture) ; and use a shader trick to move the pupil. You can find many eyes shaders in the asset store.